Problem: Simplify the following expression: $ q = \dfrac{7}{4} + \dfrac{-10p + 3}{p - 6} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{p - 6}{p - 6}$ $ \dfrac{7}{4} \times \dfrac{p - 6}{p - 6} = \dfrac{7p - 42}{4p - 24} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-10p + 3}{p - 6} \times \dfrac{4}{4} = \dfrac{-40p + 12}{4p - 24} $ Therefore $ q = \dfrac{7p - 42}{4p - 24} + \dfrac{-40p + 12}{4p - 24} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{7p - 42 - 40p + 12}{4p - 24} $ $q = \dfrac{-33p - 30}{4p - 24}$